On the one hand a curved sensor should be compatible with existing lenses, as the curve matches most lens's convex field curvature, and should produce sharper edges as a result. On the other hand, each focal length and each field curvature would have it's own optimum sensor curvature, so amount of sensor curvature would be a compromise, but still better than flat sensor. Added edge sharpness would be for 2 reasons: better fit to field curvature, and incident light angle closer